Approximation results for robust control of heat-diffusion equations

Mordukhovich (1990) and Mordukhovich and Zhang (1993) previously considered robust control problems for linear heat-diffusion equations with state constraints. Using multistep approximation procedures and taking into account special features of the problems, they obtained first-order characteristics and computed suboptimal parameters of three-positional boundary regulators. The main goal of our study is to find an appropriate feedback control law which ensures (minimax) optimality and robust stability properties of the closed-loop systems in the presence of uncertain perturbations. To the best of our knowledge, there are no results available in the general H_∞-control theory which could be directly applied to the distributed parameter systems considered under hard state-control constraints. High-order approximation results for the systems under consideration, which allow to obtain useful characteristics of suboptimal controls, are presented.